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Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

Alexandre Chapoutot 1
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems.
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https://hal.archives-ouvertes.fr/hal-00469007
Contributor : Alexandre Chapoutot <>
Submitted on : Friday, June 18, 2010 - 9:37:17 AM
Last modification on : Thursday, March 21, 2019 - 2:16:22 PM
Long-term archiving on: : Friday, September 24, 2010 - 11:01:02 AM

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Alexandre Chapoutot. Interval Slopes as Numerical Abstract Domain for Floating-Point Variables. SAS 2010 - 17th Static Analysis Symposium, Sep 2010, Perpignan, France. pp.184-200, ⟨10.1007/978-3-642-15769-1_12⟩. ⟨hal-00469007v4⟩

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